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University of California, Davis

ECN 101 – WINTER 2019

Problem Set 1

Upload on Canvas by 5 pm on January 22, 2019

Problem 1:

Do the following activities contribute to US GDP? Explain why or why not? In

which year do these activities contribute to US GDP and to which component

of expenditure?

(a) A new Toyota Camry built in Japan and sold in the US in 2019

(b) A new Toyota Camry built in Tennessee in December 2013 and sold in

Canada in January 2019

(c) A used Toyota Camry built in Japan in 2007 and sold in the US in December 2019

(d) A new Toyota Camry built in Tennessee in December 2013 and sold in

North Carolina in June of 2019

(e) A used Toyota Camry bought by a used car dealership for $5000 and sold

for $6000 in 2019

Problem 2:

Consider a country where GDP = 100, Consumption = 20, Investment = Government expenditure, and Net Exports = -50. Then, in this country the government expenditure equals:

a) 60

b) 65

c) 70

d) 80

Problem 3:

Write each production function given below in terms of output per person y ≡

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Y/L and capital per person k ≡ K/L. Plot these per person versions in a graph

with y on the vertical axis and k on the horizontal axis. (You can assume A¯ is

a constant positive number).

(a) Y = AK¯ 1/3L

2/3 and Y = AK¯ 3/4L

1/4

(plot them on the same graph).

(b) Y = K.

(c) Y = K + AL¯

(d) Y = K − AL¯

Problem 4:

If the US GDP doubles every 35 years, then the growth rate of the US GDP is:

a) 0.002

b) 0.02

c) 0.2

d) 0.035

Problem 5:

Consider the following variation of the aggregate production function. Now

firms must use oil M to produce output (in addition to labor and capital). The

price of a unit of oil is p

max Πf = AKαL

βMγ − wL − rK − pM

(a) Find a first-order condition for the firm’s demand for oil.

(b) What must be true about the parameters α, β, and γ if this production

function exhibits constant returns to scale?

(c) If the price of oil p rises, what would you expect to happen to carbon

intensity (the ratio of oil per unit output: M/Y) in this economy? What

happens to the revenue share of oil (the ratio of total oil payments to

output: pM/Y)?

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Problem 6:

Which of the following statements about the Solow model with population

growth are FALSE?

(a) An increase in the population growth rate lowers capital and output per

capita in steady state.

(b) An increase in the saving rate always raises capital per capita in steady

state.

(c) An increase in the saving rate always raises consumption per capita in

steady state.

(d) An increase in TFP raises capital and output per capita

(e) None of the above

Problem 7:

Over the last 50 years in the US, GDP per person has grown at approximately

1% per year, while capital per person has been accumulating at around 0.5%

per year. Assume a capital share of 0.3. What is the growth rate of the Solow

residual?

Problem 8:

Consider the standard Solow model. The expression for output per worker and

the dynamics of capital per worker are given by the following expression:

y = Akα

∆k = sy − δk

where δ > 0 is the depreciation rate of capital.

(a) Using a Solow diagram, what is the effect of an increase in productivity A

on steady state capital? (label the axes and mark the initial and the final

steady state level of capital)

(b) Find an algebraic expression for the steady state capital per worker.

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(c) What happens to steady state output and consumption after a positive

productivity shock? Justify your response.

(d) If the real wage equals the marginal product of labor, what is the growth

rate of the real wage in steady state?

Problem 9:

Which of the following statements about the role of institutions in economic

growth is TRUE and which of the following statements is FALSE? Explain.

(a) Higher expropriation risk due to low-quality governance and poor institutions might account for low levels of human and public capital in poor

nations

(b) The quality of institutions in countries colonized by Europeans is correlated with whether climate/disease allowed European settlers to live in

those areas

(c) Low-quality institutions make it difficult to protect property rights and

enforce contracts

(d) Low-quality institutions are central to the theory of poverty traps that

states that countries need a ‘big push’ to facilitate convergence in living

standards to the developed world

Problem 10:

The reason why the Romer model predicts sustained economic growth, unlike

the Solow model, is that

a) Ideas, unlike physical capital, are non-rivalrous

b) Ideas, unlike physical capital, do not depreciate

c) The accumulation of new ideas, unlike the accumulation of physical capital, does not run into diminishing returns to scale

d) All of the above

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